Question

The difference between two numbers is 8. Twice the number is 4 more than the larger number. What is the smaller number?

Answer 1

If the two numbers are x and y, then:

x + y = 8

18 - 2x = 4y - 2.

When we subtract y from both sides in our first equation we get:

x = 8 - y, so:

18 - 2(8 - y) = 4y - 2

18 - 16 + 2y = 4y - 2

2 + 2y = 4y - 2

2y = 4

y = 2

Since x + y = 8, and y = 2, x = 6, and since 6 > 2, the larger number is 6.